Operator-valued function space integrals via conditional integrals on an analogue Wiener space II
Bull. Korean Math. Soc. 2016 Vol. 53, No. 3, 903-924
https://doi.org/10.4134/BKMS.b150418
Published online May 31, 2016
Dong Hyun Cho
Kyonggi University
Abstract : In the present paper, using a simple formula for the conditional expectations given a generalized conditioning function over an analogue of vector-valued Wiener space, we prove that the analytic operator-valued Feynman integrals of certain classes of functions over the space can be expressed by the conditional analytic Feynman integrals of the functions. We then provide the conditional analytic Feynman integrals of several functions which are the kernels of the analytic operator-valued Feynman integrals.
Keywords : analogue of Wiener measure, conditional analytic Feynman integral, conditional analytic Wiener integral, operator-valued Feynman integral, simple formula for conditional expectation, Wiener space
MSC numbers : Primary 60H05; Secondary 28C20, 46T12
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